Mean, Median, Mode Calculator
Enter your numbers separated by commas or spaces to get the mean, median, mode and range.
The three averages
People say "average" when they could mean three different things. Each answers a different question about the centre of your data.
| Measure | How to find it | Best used when |
|---|---|---|
| Mean | Sum ÷ count | Data is evenly spread |
| Median | Middle of the sorted list | Data has outliers |
| Mode | Most frequent value | Data is categories or repeated values |
Worked example: 3, 5, 5, 7, 10
The sum is 30 and there are 5 values, so the mean is 30 ÷ 5 = 6. The list is already sorted, and the middle value is 5, so the median is 5. The value 5 appears twice, so the mode is 5. The range is the largest minus the smallest, 10 − 3 = 7.
Why the mean and median differ
Change the 10 to 100. The mean jumps to 24 but the median stays at 5. That gap tells you the data is skewed by an outlier. Reports on house prices and incomes quote the median for this reason.
Common mistakes
Finding the median without sorting first gives a wrong answer, and so does picking the middle position of an even-sized list instead of averaging the two middle values. For spread around the mean, you will also want the standard deviation calculator.
Frequently asked questions
What is the difference between mean, median and mode?
The mean is the sum divided by the count. The median is the middle value of the sorted list. The mode is the value that appears most often.
How do you find the median of an even-sized list?
Sort the numbers and average the two middle values. For 2, 4, 6, 8 the median is (4 + 6) ÷ 2 = 5.
Can a data set have more than one mode?
Yes. If two values tie for most frequent, the set is bimodal. If every value appears once, there is no mode.
When is the median better than the mean?
Use the median when the data has outliers. One very large salary pulls the mean up but barely moves the median.
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